d-dimensional Oscillating Scalar Field Lumps and the Dimensionality of Space

Marcelo Gleiser

doi:10.1016/j.physletb.2004.08.064

paper

d-dimensional Oscillating Scalar Field Lumps and the Dimensionality of Space

arXiv:hep-th/0408221 · doi:10.1016/j.physletb.2004.08.064

Abstract

Extremely long-lived, time-dependent, spatially-bound scalar field configurations are shown to exist in $d$ spatial dimensions for a wide class of polynomial interactions parameterized as $V (ϕ) = \sum_{n = 1}^{h} \frac{g _{n}}{n !} ϕ^{n}$ . Assuming spherical symmetry and if $V^{''} < 0$ for a range of values of $ϕ (t, r)$ , such configurations exist if: i) spatial dimensionality is below an upper-critical dimension $d_{c}$ ; ii) their radii are above a certain value $R_{min}$ . Both $d_{c}$ and $R_{min}$ are uniquely determined by $V (ϕ)$ . For example, symmetric double-well potentials only sustain such configurations if $d \leq 6$ and $R^{2} \geq d [3 (2^{3/2} /3)^{d} - 2]^{- 1/2}$ . Asymmetries may modify the value of $d_{c}$ . All main analytical results are confirmed numerically. Such objects may offer novel ways to probe the dimensionality of space.

In press, Physics Letters B. 6 pages, 2 Postscript figures, uses revtex4.sty

d-dimensional Oscillating Scalar Field Lumps and the Dimensionality of Space

Abstract

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